Abstract: New exact analytical bound-state solutions of the D-dimensional
Klein–Gordon equation for a large set of couplings and potential
functions are obtained via mapping onto the nonrelativistic
bound-state solutions of the one-dimensional generalized Morse
potential. The eigenfunctions are expressed in terms of generalized
Laguerre polynomials, and the eigenenergies are expressed in
terms of solutions of irrational equations at the worst. Several
analytical results found in the literature, including the so-called
Klein–Gordon oscillator, are obtained as particular cases of this
unified approach.